I have a chip that says LM1084. Not sure which version it is. I know there are 3.3, 5, 12, and adjustable voltage.

Specs say the input max voltage is 29 volts.

I am using a 25.2 volt AC transformer. Passing the secondary through a bridge rectifier and then a large capacitor ( 63 volts, 470uF electrolytic metal can ) I get 37 volts DC. I guess it is buffering the peak voltage. I put an LED circuit on it to drop the voltage, but it only dropped it down to 35.6 volts.

You don't know the output voltage of the LM1084. The max input for the 5V model is 25V. So will need to reduce the supply at least that far for testing. ((29V max is only for adjustable model!))

The LED is probably 20mA or 30mA max, while the LM1084 is a 5A max voltage regulator. So the LED rig is just for testing at low current, right? The forward voltage of LEDs is set by the color; with infrared at like 1.6V, red at 1.8V, and blue at 3.8V. Amber, yellow and green in-between.

For testing put a 1K , or so, resistor on LM1084 output to common. (To keep the current at 10mA or less.) Series connect enough LEDs (of what ever color) to drop voltage to less than 25V, connect to LM1084 input. Measure output resistor voltage. If zero (or same as input) you may have an adjustable; look on spec sheet for how to set up the adjustment.